Question

The table shows the heights y (in centimeters) of a plant after x weeks. Use the table to complete the statements.

x 0
4
8
y 17 29 41

Answer 1

Answers are

1) equation is y = 3x + 17
2) slope is rate of 3
3) y intercept is 17
4) how many weeks to reach 65 cm? 16


Step by step

Using points (0,17) and (4,29)
Find slope by using y2 - y1 over x2 - x1

29 - 17 over 4 - 0 = 12/4 simplified to 3

Your slope (m) is 3

Now using point slope form we can find the equation of the line using slope of 3 and (0, 17)

y - y1 = m (x - x1)

y - 17 = 3 (x - 0)
Distribute multiply

y - 17 = 3x

Add 17 to both sides to isolate y

y - 17 + 17 = 3x + 17
Simplify

y = 3x + 17

This is your equation for the line

Now let’s answer questions

1) equation is y = 3x + 17
2) slope is rate of 3
3) y intercept is 17
4) how many weeks to reach 65 cm?

Using our equation y = 3x + 17
we are solving for x,
we know our output (y) is 65

65 = 3x + 17

Subtract 17 from both sides to isolate x

65 - 17 = 3x
Simplify

48 = 3x

Divide both sides by 3 to solve for x

48/3 = 3/3 x

16 = x

So it will take 16 weeks
to reach 65 cm height